1. **State the problem:** We need to find the volume of a cuboid with given dimensions. 2. **Given:** - Length $l = 5$ cm - Width $w = 6$ cm - Height $h$ is 3 cm longer than the width, so $h = w + 3 = 6 + 3 = 9$ cm 3. **Formula for volume of a cuboid:** $$V = l \times w \times h$$ 4. **Substitute the values:** $$V = 5 \times 6 \times 9$$ 5. **Calculate:** $$V = 270$$ 6. **Answer with units:** The volume of the cuboid is $270$ cubic centimeters (cm$^3$).